\section{Bit Depth}

Bit depth is a term commonly used in digital audio. It plays a similar role in images and videos- it is the spectrum of bits that is available to determine the resolution of a processed data; the higher the bit depth is, (e.g. 24 bit) the more flexible and accurate the processing will be. On the contrary, having low bit depth (e.g. 16 bit) means  the output will be more inaccurate, in addition to some frequencies being consequently lost in the process \cite{bit.depth1}. In other notes, quantization is the process which maps the audio inputs, while bit depth is the range of levels which can be accounted during quantization. 

With a 16-bit sequence, there are 65,536 possible levels. With every additional bit, there is double the amount of levels. When there is 24-bit process or piece of 24-bit hardware, there are 16,777,216 available levels of audio. 24-bit is the recommended bit depth for capturing the full dynamic range\cite{bit.depth2}.


\section{Quantization}

When converting analog signals to its digital counterpart, quantization is the conversion, where the continuous signal goes into a discrete though bit depth, where quantization rounds of the continuous signal in to the nearest bit number in the sample. And there for moves the analog signal in to the digital world. Since quantization rounds of the continuous signal the discrete signal is not a one to one version, with the original input\cite{quant}. 


\section{Nyquist Theorem}

The Nyquist Theorem, also known as the 'sampling theorem', is a concept that is involved in the conversion of analog-to-digital signals and anti-aliasing. In order for analog-to-digital conversion (ADC) to result with copy of the input acoustic energy, the sampling of the acoustic waveform must be taken frequently See figure \ref{fig:Sampling}. 

According to the Nyquist Theorem, the sampling rate must be at least, twice the maximum
( 2fmax) analog input in order to extract all of the information from the bandwidth and accurately correspond to the input acoustic energy. Consequently, there is a risk of some of the higher frequency components of analog input signal not being correctly represented in the digitized output, if the sampling rate is less than 2fmax,. Thus, if one wishes to process signals from 20Hz to 20,000Hz from analog input to CD, the frequency must be sampled at a rate of 40,000Hz to reproduce a 20,000Hz signal. By default, the CD standard is to sample 44,100 times per second, or 44.1 kHz\cite{nyquist1}.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.50\textwidth]{images/sa4.jpg}
\caption{A comparison between an accurately sampled and under-sampled signal \cite{image.sampling}}
\label{fig:Sampling}
\end{figure}

Furthermore, when a digital signal is reconverted to analog form by a digital-to-analog converter, frequency components that were not present in the original analog input can be generated. This undesirable condition is a form of distortion called aliasing\cite{nyquist2}.




